Question

Brianna needs to buy 3 new work uniforms, which consist of a hat and shirt. Each shirt is $12.50, and the total for her purchase is $62.25. She writes the following equation to help figure out the cost of each hat.
3(c+12.50)=62.25
She solves the equation to get c=8.25.
How could Brianna correctly solve this problem without using the equation?
Responses
Divide $12.50 by 3. Then, subtract the quotient from $62.25. Finally, divide the sum by 3.


Multiply 3 by $12.50. Then, subtract the product from $62.25. Finally, divide the difference by 3.


Divide $12.50 by 3. Then, subtract the quotient from $62.25. Finally, multiply the sum by 3.


Multiply 3 by $12.50. Then, add the product to $62.25. Finally, divide the sum by 3.

Answer 1

To determine the cost of each hat without using an equation, Brianna can follow these steps logically:

1. **Calculate the total cost of the shirts**: Since each shirt costs $12.50 and she is buying 3 shirts, we multiply:
\[
3 \times 12.50 = 37.50.
\]

2. **Determine the total cost of the hats**: The total amount spent on the uniforms is $62.25. To find out how much was spent on the hats, we subtract the total cost of the shirts from the total cost:
\[
62.25 - 37.50 = 24.75.
\]

3. **Calculate the cost of each hat**: Since there are 3 hats, divide the total cost of the hats by 3:
\[
\frac{24.75}{3} = 8.25.
\]

Let's analyze the response options given:

1. **Divide $12.50 by 3. Then, subtract the quotient from $62.25. Finally, divide the sum by 3.** (Incorrect)

2. **Multiply 3 by $12.50. Then, subtract the product from $62.25. Finally, divide the difference by 3.** (Correct)

3. **Divide $12.50 by 3. Then, subtract the quotient from $62.25. Finally, multiply the sum by 3.** (Incorrect)

4. **Multiply 3 by $12.50. Then, add the product to $62.25. Finally, divide the sum by 3.** (Incorrect)

Therefore, the correct process Brianna could have used is the second option: **Multiply 3 by $12.50. Then, subtract the product from $62.25. Finally, divide the difference by 3.**